Experimental and numerical study of heat transfer in horizontal concentric annulus containing phase change material

Canadian Journal of Chemical Engineering, August, 2008 by Ritabrata Dutta, Arnab Atta, Kumar Tapas Dutta

INTRODUCTION

In many engineering applications such as thermal energy storage using phase change materials (PCMs), the melting and solidification are important phenomena. Melting of the phase-change material gives rise to natural convection, while the flow structure could significantly affect phase change process. The essential feature of melting (or solidification) of PCM is the existence of the moving interface between two phases with time. The convection influences the morphology of this solid-liquid interface. This problem was studied as early as in 1831 by Lame and Clapeyron (Huntler and Kutter, 1989). The sequence of papers written by Stefan has given his name to this type of problem as "Stefan problem." The problem of heat transfer with phase change can be formulated, considering either the temperature or the enthalpy as the dependent variable. When temperature is considered as dependent variable, the energy equations for both the phases are to be written independently and then coupled for the interface. In fact this technique requires the knowledge of the interface position explicitly for the determination of temperature, complicating the formulation and method of solution. The problem has been solved by a method of immobilization of the interface (Duda et al., 1975). When the enthalpy is considered as the dependent variable the knowledge of the interface position is not required and a single enthalpy equation for the whole domain suffices. Huntler and Kutter (1989) demonstrated the enthalpy method for heat transfer problems with moving boundaries associated with phase change. Pannu et al. (1980) calculated temperature and velocity profiles, rates of heat transfer, movements of melting interface in vertical and horizontal cylinders by finite difference method. The integral method has been applied to study the effects of natural convection on the melting of solid around the horizontal cylinder (Yao and Chen, 1980; Yao and Cherney, 1981). The perturbation and numerical solution of melting around the heated horizontal cylinder for an isothermal boundary condition were studied previously (Reiger et al., 1982; Prusa and Yao, 1984a,b) and the melting process in a rectangular enclosure driven by coupling of heat conduction in the solid phase and natural convection in the melt of the PCM has been analyzed (Bernard et al., 1986). Viswanath and Jaluria (1993, 1995) carried out a numerical modelling of the macroscopic melting processes in rectangular enclosures using an enthalpy--porosity formulation and has been used to circumvent the need to track the moving interface at every time instant. In this case a single energy equation is valid over all regions including the interface. The SIMPLE algorithm was employed to implement the solution. A numerical study of melting of PCM around a horizontal circular cylinder of constant wall temperature and in presence of natural convection in melt region was presented by Ismail and da Silva (2003a,b). In a recent literature (Lamberg et al., 2003), the comparison of experimental data with numerical results was obtained where only energy equation was solved by modelling convective source term with an effective heat capacity method. Ettouney et al. (2005) studied heat transfer characteristics of PCM in a vertical annulus and developed empirical correlations involving Nusselt number, Rayleigh number, Steffan number, and Fourier number.

Ng et al. (1998) in their study employed the finite element method to simulate the convection dominated melting of a PCM in a cylindrical horizontal annulus heated isothermally from an inside wall. The effects of Rayleigh number on the melting rate as well as the evolution of the flow pattern were examined. The authors observed that the increasing Rayleigh number promotes the heat transfer rate and the multiple cellular pattern was found to occur at high Rayleigh number (>[10.sup.6]). Khillairkar et al. (2000) studied melting in a concentric horizontal annulus of arbitrary geometric arrangement such as external square tube with circular tube inside (Type A) and circular external tube with a square tube inside (Type B). The authors studied the effects of the Rayleigh numbers as well as the heating of either the inside surface or the outside surface and in some cases both the surfaces at a temperature above the melting point of the PCM. To account for the physics of the time wise evolution of flow at the solid--liquid interface the well known enthalpy--porosity model was employed in the fixed grid method. For both the horizontal annuli of Type A and Type B, it is observed that the effects of heating both the surfaces is the same as the heating of inside surface or the outside surface separately until there is an interaction between the two melt-zone. It is observed that the melting rate is faster due to good mixing between melt zones. This suppresses the thermal stratification attained in the horizontal annuli of both Type A and B. The thermal stratification occurs in the upper part of the cavity due to the fact that the energy charged to the system is mainly carried upward by the free convection. Thus, the energy is used to raise the temperature of the melt instead of melting the PCM. So, the energy storage in the system is more in the form of sensible heat than in the form of latent heat. Balikowski and Mollendorf (2007) recently studied the performance of PCM in a horizontal annulus of a double pipe heat exchanger in a water circulating loop. PCM was placed in the annular region of a double pipe heat exchange with water circulated in the inside pipe. Experiments were performed in which the PCM would absorb or release heat at various temperatures and water flow rates. The effect of different water flow rates on the heat transfer rates were examined. The difference between temperature of hot water and melting point of the PCM was between 2 and 6[degrees]C. To avoid any thermal penalty and the flow rate of hot water were so maintained that there was virtually no difference between the inlet and outlet hot water temperatures.